Expert Answer to "What is the derivative of ( 4 +..."

College
Calculus and Analysis
Differential Calculus
Derivatives

anniferathonniz8km

Answered question

2022-04-04

What is the derivative of

(4 + 3 x) ﻿ x^{2}

Answer & Explanation

hospitaliapbury

Beginner2022-04-05Added 25 answers

Differentiate using the Product Rule which states that $\frac{d}{d x} [f (x) g (x)]$ is $f (x) \frac{d}{d x} [g (x)] + g (x) \frac{d}{d x} [f (x)]$ where $f (x) = 4 + 3 x$ and $g (x) = x^{2}$ .

$(4 + 3 x) \frac{d}{d x} [x^{2}] + x^{2} \frac{d}{d x} [4 + 3 x]$

Differentiate.

$2 (4 + 3 x) x + 3 \cdot x^{2}$

Simplify.

$9 x^{2} + 8 x$

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